Question

How do you find the linearization of `f(x) = 1/sqrt(2+x)` at the point a=0?

Answer 1

Linearization is finding the linear approximation to a function at a given point `y=f(a)+f'(a)(x-a)`

Explanation:

`f'(x)=-1/2(2+x)^(-3/2)`
`f'(0)=-1/2(2+0)^(-3/2)=-0.18`
`f(0)=1/sqrt(2)=0.71`
`f(0)~=f(0)+f'(0)*(x-0)=0.71-0.18*x`